Epsom can actually dehydrate bacteria either on the fish or in the fish's guts, this is a bit more effective than salt for curing purposes. Salt actually makes the water naturally aerate more as well as retards the growth of most fresh-water bacteria.
Generally in a weakened fish I don't like to use either but for one starting out healthy that gets infected either OR both work fine. The ratios for using both get a little tricky, colder water uses more epsom, warmer more salt but you don't use full dose of either.
The gap between the mineral treatments and aeration treatment is where Lifeguard is intended to be used. It uses a suspension form of chlorine that tricks bacteria into eating it, then the chlorine eats the bacteria. The opposite of Lifeguard is Potassium Permanganate... KMnO4 sucks oxygen out of the water violently, creating a suddenly anaerobic environment. If you let the KMnO4 sit mixed with water for too long it simply becomes a mineral contaminant in the water, one that a fish's kidneys are ill prepared to deal with. High ammonia and nitrite also have some antibiotic properties with the exception of nitrosomonas and nitrospira but they're also toxic to fish. Nitrate itself seems to do nothing but be beneficial to fungus. With all the chemicals in this paragraph you're at risk for kidney damage. Fish swallow the water with their food and some transfers into their blood simply from aspiration. It is an interesting note that with betta you can actually dip them in high nitrite water as an antibiotic treatment (not something any of us keep on hand, I'm sure) to kill aerobic bacteria without any long term effects like Permanganate can have. It takes time for nitrite toxicity to build up in betta and only seconds for it to affect other fish. (5ppm nitrite un-buffered will nearly instantly kill most tetra but your betta will likely live more than a day in it before succumbing, simply because of the labyrinth gland.)
I'm a bit off the primary topic here, I know, but there's a few more tidbits about ammonia and nitrite that need to be added. Both are great for growing plants and both are great for growing aerobic fungus. This is why it is important to keep both to a minimum, either with daily water changes using prime or with actual biological nitrification processing. Nitrate is not so handy for fungus while still handy for plants.